Abstract

this paper, we focus on the translation modeling problem. Before we turn to this problem, however, we should address an issue that may be a concern to some readers: Why do we estimate Pr(e) and Pr(fle) rather than estimate Pr(elf ) directly? We are really interested in this latter probability. Wouldn't we reduce our problems from three to two by this direct approach? If we can estimate Pr(fle) adequately, why can't we just turn the whole process around to estimate Pr(elf)? To understand this, imagine that we divide French and English strings into those that are well-formed and those that are ill-formed. This is not a precise notion. We have in mind that strings like Il va la bibliothque, or I live in a house, or even Colorless green ideas sleep furiously are well-formed, but that strings like lava I1 bibliothque or a I in live house are not. When we translate a French string into English, we can think of ourselves as springing from a well-formed French string into the sea of well-formed English strings with the hope of landing on a good one. It is important, therefore, that our model for Pr(elf ) concentrate its probability as much as possible on wellformed English strings. But it is not important that our model for Pr(fle ) concentrate its probability on well-formed French strings. If we were to reduce the probability of all well-formed French strings by the same factor, spreading the probability thus 265 liberated over ill-formed French strings, there would be no effect on our translations: the argument that maximizes some function f(x) also maximizes cf(x) for any positive constant c. As we shall see below, our translation models are prodigal, spraying probability all over the place, most of it on ill-formed French strings. In fact, as we discuss in Section 4.5, two...

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